Renormalon-based resummation of Bjorken polarised sum rule in holomorphic QCD

Approximate knowledge of the renormalon structure of the Bjorken polarised sum rule (BSR) (Gamma) over bar (p-n)(1) (Q2) leads to the corresponding BSR characteristic function that allows us to evaluate the leading-twist part of BSR. In our previous work [1], this evaluation (resummation) was performed using perturbative QCD (pQCD) coupling a(Q(2)) = alpha(s)(Q(2))/pi in specific renormalisation schemes. In the present paper, we continue this work, by using instead holomorphic couplings [a(Q(2)) bar right arrow (Q(2))] that have no Landau singularities and thus require, in contrast to the pQCD case, no regularisation of the resummation formula. The D = 2 and D = 4 terms are included in the Operator Product Expansion (OPE) of inelastic BSR, and fits are performed to the available experimental data in a specific interval (Q(min)(2), Q(max)(2)) where Q(max)(2) = 4.74 GeV2. We needed relatively high Q(min)(2) approximate to 1.7 GeV2 in the pQCD case since the pQCD coupling a(Q(2)) has Landau singularities at Q(2) less than or similar to 1 GeV2. Now, when holomorphic (AQCD) couplings A(Q(2)) are used, no such problems occur: for the 3 delta AQCD and 2 delta AQCD variants the preferred values are Q(min)(2) approximate to 0.6 GeV2. The preferred values of alpha(s) in general cannot be unambiguously extracted, due to large uncertainties of the experimental BSR data. At a fixed value of alpha(s)(MS) over bar (M-Z(2)), the values of the D= 2 and D = 4 residue parameters are determined in all cases, with the corresponding uncertainties.